Abstract
The DPLL approach to the Boolean satisfiability problem (SAT) is a combination of search for a satisfying assignment and logical deduction, in which each process guides the other. We show that this approach can be generalized to a richer class of theories. In particular, we present an alternative to lazy SMT solvers, in which DPLL is used only to find propositionally satisfying assignments, whose feasibility is checked by a separate theory solver. Here, DPLL is applied directly to the theory. We search in the space of theory structures (for example, numerical assignments) rather than propositional assignments. This makes it possible to use conflict in model search to guide deduction in the theory, much in the way that it guides propositional resolution in DPLL. Some experiments using linear rational arithmetic demonstrate the potential advantages of the approach.
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References
Barrett, C., Deters, M., Oliveras, A., Stump, A.: Design and results of the 4th annual satisfiability modulo theories competition, SMT-COMP 2008 (2008) (to appear)
Barrett, C., Sebastiani, R., Seshia, S., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, ch. 8. IOS Press, Amsterdam (2009)
Bjørner, N., Dutertre, B., de Moura, L.: Accelerating lemma learning using joins - DPPL(⊔). In: LPAR (2008)
Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T.A., Ranise, S., van Rossum, P., Sebastiani, R.: Efficient satisfiability modulo theories via delayed theory combination. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 335–349. Springer, Heidelberg (2005)
Cooper, D.C.: Theorem proving in arithmetic without multiplication. Machine Intelligence 7, 91–99 (1972)
Cotton, S.: Algebraic satisfiability solving. Personal communication (2009)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communications of the ACM 5(7), 394–397 (1962)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7(3), 201–215 (1960)
Een, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)
Flanagan, C., Joshi, R., Ou, X., Saxe, J.B.: Theorem proving using lazy proof explication. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 355–367. Springer, Heidelberg (2003)
Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast decision procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)
Goldwasser, D., Strichman, O., Fine, S.: A theory-based decision heuristic for DPLL(T). In: FMCAD, pp. 1–8 (2008)
Koppensteiner, P., Veith, H.: A novel SAT procedure for linear real arithmetic. In: PDPAR (2005)
Korovin, K., Voronkov, A.: Integrating linear arithmetic into superposition calculus. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 223–237. Springer, Heidelberg (2007)
Strichman, O., Seshia, S.A., Bryant, R.E.: Deciding separation formulas with sat. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 209–222. Springer, Heidelberg (2002)
Wang, C., Gupta, A., Ganai, M.K.: Predicate learning and selective theory deduction for a difference logic solver. In: DAC, pp. 235–240 (2006)
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McMillan, K.L., Kuehlmann, A., Sagiv, M. (2009). Generalizing DPLL to Richer Logics. In: Bouajjani, A., Maler, O. (eds) Computer Aided Verification. CAV 2009. Lecture Notes in Computer Science, vol 5643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02658-4_35
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DOI: https://doi.org/10.1007/978-3-642-02658-4_35
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